An imaging system consists of a device, or a group of devices, that captures or displays an image of a subject or object. Common forms of imaging systems include televisions, computer monitors and digital cameras.
The spatial frequency response (SFR) of an imaging system is a measure of the ability of the system to capture or reproduce the spatial details of an object. This can take a number of specific forms. For a spatially invariant imaging system, one commonly used form of spatial frequency response measure is the ‘optical transfer function’ (OTF). The OTF can be calculated as the Fourier transform of the point spread function (PSF), sometimes known as the impulse response function. The OTF is complex, consisting of a magnitude part (the modulation transfer function) and a phase part (the phase transfer function). The modulus of the OTF, called the modulation transfer function (MTF), is a measure of the effectiveness with which a device captures or represents different spatial frequencies without regard to any phase shifts that the system produces. This is often used instead of the OTF since it is easier to measure.
It is known that the MTF of an imaging system can be measured using a sine wave test pattern. The Fourier transform of the measured sine wave is calculated from a region of the test pattern, and the modulation amplitude is compared to the modulation amplitude of the input sine wave to calculate the modulation transfer function. However this approach relies on the imaging system being spatially invariant since the calculation of the MTF must use information from an extended region of the test pattern.
More commonly, MTF is measured using test patterns consisting of geometric shapes with high contrast sharp edges. This produces a measurement of the edge spread function (ESF). The gradient of the ESF normal to the edge gives the line spread function (LSF). The Fourier transform of the LSF is computed to obtain the MTF. However this approach also relies on the imaging system being spatially invariant since the calculation of the MTF must use information from an extended region of the test pattern.
If a system is not spatially invariant, which is often the case for real systems, then the OTF and MTF are not strictly defined. In the past, this situation has been handled only if the system is approximately spatially invariant over some local region. The OTF is then determined locally assuming spatial invariance over the region analysed, but the analysis requires relatively large regions to achieve accurate results. It is therefore only possible to determine the SFR at a limited number of locations and it is likely to be affected by any deviation from the assumed spatial invariance. What is desired is a spatially variable measure of SFR and a method whereby measurements can be made locally at a single point.